Deconvolution of 3-D Gaussian kernels

Abstract

Ulmer and Kaissl formulas for the deconvolution of one-dimensional Gaussian kernels are generalized to the three-dimensional case. The generalization is based on the use of the scalar version of the Grad's multivariate Hermite polynomials which can be expressed through ordinary Hermite polynomials.

Large‐wavelength Gaussian deconvolution phase‐contrast computed tomography for THz continuous wave (0.11 THz)

“…Gaussian deconvolution is specifically investigated for the restoration. 33 General Gaussian convolution can be written as…”

“…Distortions and blurring will deteriorate the quality of reconstructed images on account of ray‐based phase‐used Radon transform under Gaussian beam, necessitating the restoration from Gaussian beam to ray. Gaussian deconvolution is specifically investigated for the restoration 33 . General Gaussian convolution can be written as $$$R(\overrightarrow{r})={\int }_{-\infty }^{+\infty }G(\overrightarrow{r}-\overrightarrow{\xi },\sigma )S(\overrightarrow{\xi })d\overrightarrow{\xi }$$$where $$R(\vec{r})$$ is the pixel of reconstructed images, $$G(\vec{r}-\vec{\xi },\sigma )$$ is the Gaussian convolution kernel, $$S(\vec{\xi })$$ is the pixel of real samples, $$\vec{r}$$ and $$\vec{\xi }$$ denote the positions, $$\sigma $$ means the resolution limit.…”